Pith Number

pith:6RRZ3S6Y

pith:2025:6RRZ3S6YYDESYLPR3AMU3DFDYA

not attested not anchored not stored refs pending

Subgraph Entropy

Matt Clay, Tarik Aougab, Tawfiq Hamed

arxiv:2506.18838 v3 · 2025-06-23 · math.GT · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6RRZ3S6YYDESYLPR3AMU3DFDYA}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-06-04T01:09:37.772990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4639dcbd8c0c92c2df1d8194d8ca3c02b530895d7ccd3eb3211fdea8f14cbfc

Aliases

arxiv: 2506.18838 · arxiv_version: 2506.18838v3 · doi: 10.48550/arxiv.2506.18838 · pith_short_12: 6RRZ3S6YYDES · pith_short_16: 6RRZ3S6YYDESYLPR · pith_short_8: 6RRZ3S6Y

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6RRZ3S6YYDESYLPR3AMU3DFDYA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f4639dcbd8c0c92c2df1d8194d8ca3c02b530895d7ccd3eb3211fdea8f14cbfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca6e7c5ec7a08f1f47e9a60704ce5dde8c84ed8b692603bf6c16221a414e9a8b",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-06-23T16:57:40Z",
    "title_canon_sha256": "14604b593f433446958a5ecf40275c4e6b0c99c3a3686d050badc29fc2258279"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.18838",
    "kind": "arxiv",
    "version": 3
  }
}